1. Neave sought to clean up the corruption within the security services.

2. Neave was killed by a bomb.

Gerald James, former chief of the armaments firm Astra Holdings, wrote that the mercury switch on the bomb was only available to the CIA at the time.

3. Enoch Powell claimed that the CIA wanted a united Ireland within NATO.

Former UK cabinet minister Tony Benn, who supported the CIA's aim of the unification of Ireland

From Wikipedia we learn:

UK politician Tony Benn records in his diary (17 February 1981) that a journalist from the New Statesman, Duncan Campbell, told him that he had received information from an intelligence agent two years previously that Neave had planned to have Benn assassinated, if there was a possibility that Benn might be elected Labour Party Leader.

The New Statesman printed the story on 20 February 1981, naming the agent as Lee Tracey.

Tracey claimed to have met Neave and was asked to join a team of intelligence and security specialists which would "make sure Benn was stopped".

Tracey planned a second meeting with Neave but Neave was killed before they could meet again.[8]

Kevin Cahill, an Irish investigative journalist, claims Neave was on the verge of a massive overhaul of the security services, possibly involving a merger of MI5 and MI6 and arising from his belief in corruption in the security services.

Cahill claims that Neave would have been head of the combined security services with Sykes and Tugendhat as his deputies, with Sykes responsible for foreign operations and Tugendhat responsible for home operations.

Cahill concluded that Neave was murdered by MI6 agents working with the CIA because Neave sought to prosecute senior figures in the intelligence establishment for corruption.[9]

On 18 October 1986 Enoch Powell returned to the subject of Neave's death in a speech to Conservative students in Birmingham.

He told them that INLA had not killed Neave, but that he had been assassinated by "MI6 and their friends".

Powell claimed Neave's Northern Ireland policy had been one of integration with the rest of the UK.

His murder, alleged Powell, was intended to make the British Government adopt a policy more acceptable to America in her aim of a united Ireland within NATO.[11]